In his thesis Bachelier introduces Brownian motion as a tool for the analysis of Recensioner i media "I believe that this is an excellent text for undergraduate or MBA classes on Mathematical Finance. The bulk of the book describes a model with finitely many, discrete trading dates, and a finite sample space, thus it avoids the technical difficulties associated with continuous time models. The major strength of this book is its careful balance of mathematical rigor and intuition. He is noted for his fundamental research on the mathematical and economic theory of security prices, especially his development of important bridges between stochastic calculus and arbitrage pricing theory as well as his discovery of the risk neutral computational approach for portfolio optimization problems.
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Finance - Mathematical models. Single Period Securities Markets. Model Specifications. Arbitrage and Other Economic Considerations. Risk Neutral Probability Measures. Valuation of Contingent Claims.
Complete and Incomplete Markets. Risk and Return 2. Single Period Consumption and Investment. Optimal Portfolios and Viability. Risk Neutral Computational Approach. Consumption Investment Problems. Mean-Variance Portfolio Analysis. Optimal Portfolios in Incomplete Markets. Equilibrium Models 3. Multiperiod Securities Markets. Model Specifications, Filtrations, and Stochastic Processes. Return and Dividend Processes. Conditional Expectation and Martingales. Economic Considerations. The Binomial Model.
Markov Models 4. Options, Futures, and Other Derivatives. Contingent Claims. European Options Under the Binomial Model. American Options. Forward Prices and Cash Stream Valuation. Futures 5. Optimal Consumption and Investment Problems. Optimal Portfolios and Dynamic Programming. Optimal Portfolios and Martingale Methods. Consumption-Investment and Dynamic Programming. Consumption-Investment and Martingale Methods. Maximum Utility from Consumption and Terminal Wealth. Optimal Portfolios with Constraints.
Optimal Consumption-Investment with Constraints. Portfolio Optimization in Incomplete Markets 6. Bonds and Interest Rate Derivatives. The Basic Term Structure Model. Lattice, Markov Chain Models. Yield Curve Models. Forward Risk Adjusted Probability Measures.
Coupon Bonds and Bond Options. Swaps and Swaptions. Caps and Floors 7. Models with Infinite Sample Spaces. Finite Horizon Models. Infinite Horizon Models. Appendix: Linear Programming.
Introduction to Mathematical Finance
Introduction to mathematical finance: Discrete time models